TY - CONF
TI - A categorical approach to probability theory
AU - Giry, MichÃ¨le
A2 - Banaschewski, B.
T3 - Lecture Notes in Mathematics
C1 - Berlin, Heidelberg
C3 - Categorical Aspects of Topology and Analysis
DA - 1982///
PY - 1982
DO - 10/dtx5t5
DP - Springer Link
SP - 68
EP - 85
LA - en
PB - Springer
SN - 978-3-540-39041-1
KW - Categorical probability theory
ER -
TY - CONF
TI - On Geometry of Interaction
AU - Girard, Jean-Yves
A2 - Schwichtenberg, Helmut
T3 - NATO ASI Series
AB - The paper expounds geometry of interaction, for the first time in the full case, i.e. for all connectives of linear logic, including additives and constants. The interpretation is done within a C*-algebra which is induced by the rule of resolution of logic programming, and therefore the execution formula can be presented as a simple logic programming loop. Part of the data is public (shared channels) but part of it can be viewed as private dialect (defined up to isomorphism) that cannot be shared during interaction, thus illustrating the theme of communication without understanding. One can prove a nilpotency (i.e. termination) theorem for this semantics, and also its soundness w.r.t. a slight modification of familiar sequent calculus in the case of exponential-free conclusions.
C1 - Berlin, Heidelberg
C3 - Proof and Computation
DA - 1995///
PY - 1995
DO - 10/fr557p
DP - Springer Link
SP - 145
EP - 191
LA - en
PB - Springer
SN - 978-3-642-79361-5
KW - Interactive semantics
KW - Linear logic
ER -
TY - CONF
TI - Bisimulation for probabilistic transition systems: A coalgebraic approach
AU - de Vink, E. P.
AU - Rutten, J. J. M. M.
A2 - Degano, Pierpaolo
A2 - Gorrieri, Roberto
A2 - Marchetti-Spaccamela, Alberto
T3 - Lecture Notes in Computer Science
AB - The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendier in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation.
C1 - Berlin, Heidelberg
C3 - Automata, Languages and Programming
DA - 1997///
PY - 1997
DO - 10/fcqzmk
DP - Springer Link
SP - 460
EP - 470
LA - en
PB - Springer
SN - 978-3-540-69194-5
ST - Bisimulation for probabilistic transition systems
KW - Categorical probability theory
KW - Coalgebras
KW - Denotational semantics
KW - Probabilistic transition systems
KW - Transition systems
ER -